While these analytic priors have been successfully applied in many applications, they do not always adequately model the prior knowledge available in an individual problem. For example, in quantitative MR imaging of the brain employed conventional prior distributions do not truly reflect the structure of the brain [1]}. Generative models from machine learning using modern architectures such as generative adversarial networks (GANs) [2]} or variational auto-encoders (VAEs) [3]}, on the other hand, have proven to generate data that closely resemble the properties of data in a training set.
Their efficiency, adaptability and easy accessibility in standard libraries result in a multitude of applications. From speech synthesis [4]} over text generation [5]} to molecule generation [6]} and urbanization [7]}, to mention but just a few.
For a comprehensive overview on the usage of deep learning methods for the solution of linear inverse problems we refer to [8]}, and for a review on the application of data-driven models to [9]}. For an overview of generative models in computer vision see for instance [10]}, [11]}, [12]}, and for a review in medical imaging cf. [13]}.
